Multiscale estimation of GPS velocity fields

Abstract

We present a spherical wavelet-based multiscale approach for estimating a spatial velocity field
\non the sphere from a set of irregularly spaced geodetic displacement observations. Because
\nthe adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities
\nsuch as dilatation rate, strain rate and rotation rate can be directly computed using the same
\ncoefficients. In a series of synthetic and real examples,we illustrate the benefit of themultiscale
\napproach, in particular, the inherent ability of the method to localize a given deformation field
\nin space and scale as well as to detect outliers in the set of observations. This approach has
\nthe added benefit of being able to locally match the smallest resolved process to the local
\nspatial density of observations, thereby both maximizing the amount of derived information
\nwhile also allowing the comparison of derived quantities at the same scale but in different
\nregions.We also consider the vertical component of the velocity field in our synthetic and real
\nexamples, showing that in some cases the spatial gradients of the vertical velocity field may
\nconstitute a significant part of the deformation. This formulation may be easily applied either
\nregionally or globally and is ideally suited as the spatial parametrization used in any automatic
\ntime-dependent geodetic transient detector.